Why is phenyl shift preferred over methyl shift in cumene hydroperoxide reaction?

In the cumene process, which converts cumene to phenol and acetone, there is a step where cumene hydroperoxide undergoes acid-catalyzed rearrangement:

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Why does the phenyl shift happen preferentially? The methyl group is smaller and should have a higher migratory aptitude.

Phenyl shifts do not usually happen by the normal 1,2-sigmatropic "hop". Instead, the phenyl group shifts by more of a "walk". It's not really a sigmatropic rearrangement. First, one of the $\pi$-bonds in the phenyl group can attack the electrophilic center. This leads to formation of a spirobicyclic intermediate where the cation is delocalized throughout the rest of the ring. Then, the three-member ring breaks open at the expense of a carbon-carbon bond to rearomatize the phenyl ring and form the new resonance stabilized cation.